PDF Water Hammer - KSB

[Pages:34]KSB Know-how, Volume 1

Water Hammer

Table of Contents

Contents

Page 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3 2 General - The Problem of Water Hammer . . . . . . . . . . . . . .4 2.1 Steady and Unsteady Flow in a Pipeline . . . . . . . . . . . . . . . .4 3 Water Hammer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6 3.1 Inertia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6 3.2 Elasticity of Fluid and Pipe Wall . . . . . . . . . . . . . . . . . . . . . .7 3.3 Resonance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . 10 4 The Joukowsky Equation . . . . . . . . . . . . . . . . . . . . . . . . . .11 4.1 Scope of the Joukowsky Equation . . . . . . . . . . . . . . . . . . .12 5 Numerical Simulation of Water Hammer . . . . . . . . . . . . . .15 5.1 Accuracy of Numerical Surge Analysis . . . . . . . . . . . . . . . .15 5.2 Forces Acting on Pipelines as a Result of Water Hammer . .16 6 Computerised Surge Analysis . . . . . . . . . . . . . . . . . . . . . . 17 6.1 Technical Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .17 6.2 Interaction between Ordering Party and Surge Analyst . . .17 7 Advantages of Rules of Thumb and Manual Calculations .18 8 Main Types of Surge Control . . . . . . . . . . . . . . . . . . . . . . .20 8.1 Energy Storage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .20 8.1.1 Air Vessels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .20 8.1.2 Standpipes, One-Way Surge Tanks . . . . . . . . . . . . . . . . . . .21 8.1.3 Flywheels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .22 8.2 Air Valves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23 8.3 Actuated Valves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23 8.4 Swing Check Valves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .24 9 Case Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .25 9.1 Case Study: Long-Distance Water Supply System . . . . . . . .25 9.2 Case Study: Stormwater Conveyance Pipeline . . . . . . . . . .26

Model Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .26 Calculation of Actual Duty Data, First Results . . . . . . . . .27 Surge Control Measures . . . . . . . . . . . . . . . . . . . . . . . . . . .28 10 Additional Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . .30 Authors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .30

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Introduction

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1 Introduction

Most engineers involved in the planning of pumping systems are familiar with the terms "hydraulic transient", "surge pressure" or, in water applications, "water hammer". The question as to whether a transient flow or surge analysis is necessary during the planning phase or not is less readily answered. Under unfavourable circumstances, damage due to water hammer may occur in pipelines measuring more than one hundred metres and conveying only several tenths of a litre per second. But even very short, unsupported pipelines in pumping stations can be damaged by resonant vibrations if they are not properly anchored. By contrast, the phenomenon is not very common in building services systems, e.g. in heating and drinking water supply pipelines, which typically are short in length and have a small cross-section.

The owners or operators of systems affected by water hammer are usually reluctant to pass on information about any surge damage suffered. But studying the photos taken of some "accidents" (Figs. 1-a, 1-b, 1-c) one

thing is clear: the damage caused by water hammer by far exceeds the cost of preventive analysis and surge control measures.

The ability to provide reliably designed surge control equipment, such as an air vessel or accumulator1, flywheel and air valve, has long been state of the art. The technical instruction leaflet W 303 "Dynamic Pressure Changes in Water Supply Systems" published by the German Association of the Gas and Water Sector clearly states that pressure transients have to be considered when designing and operating water supply systems, because they can cause extensive damage. This means that a surge analysis to industry standards has to be performed for every hydraulic piping system at risk from water hammer. Dedicated software is available for this purpose ? an important tool for the specialist surge analyst to use. Consultants and system designers are faced with the following questions, which we hope to answer in this brochure:

? How can we know whether there is a risk of water hammer or not?

? How significant are approximation formulas for calculating water hammer?

? Can the surge analysis of one piping system be used as a basis for drawing conclusions for similar systems?

? Which parameters are required for a surge analysis?

? What does a surge analysis cost?

? How reliable is the surge control equipment available and how much does it cost to operate it?

? How reliable is a computerised analysis?

System designer and surge analyst have to work together closely to save time and money. Water hammer is a complex phenomenon; the purpose of this brochure is to impart a basic knowledge of its many aspects without oversimplifying them.

Fig. 1-a: Completely destroyed DN 600 discharge pipe (wall thickness 12 mm)

Fig. 1-b: Destroyed support (double T profile 200 mm, permanently deformed)

Fig. 1-c: DN 800 check valve following a pressure surge in the discharge pipe

1 Air vessels, sometimes also called "accumulators", store potential energy by accumulating a quantity of pressurised hydraulic fluid in a suitable enclosed vessel.

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2

General ? The Problem of Water Hammer

2 General ? The problem of water hammer

2.1 Steady and unsteady flow in a pipeline

When discussing the pressure of a fluid, a distinction has to be made between pressure above atmospheric [p bar], absolute pressure [p bar(a)] and pressure head h [m]. Pressure head h denotes the height of a homogeneous liquid column which generates a certain pressure p. Values for "h" are always referred to a datum, (e.g. mean sea level, axial centreline of pipe and pipe crown etc.).

As a rule, system designers start by determining the steady-state operating pressures and volume rates of flow. In this context, the term steady2 means that volume rates of flow, pressures and pump speeds do not change with time. Fig. 2.1-a shows a typical steady flow profile:

With a constant pipe diameter and a constant surface roughness of the pipe's inner walls, the pressure head curve will be a straight line. In simple cases, a pump's steady-state operating point can be determined graphically. This is done by determining the point where the pump curve intersects the piping characteristic.

A pumping system can never be operated in steady-state condition all the time, since starting up and stopping the pump alone will change the duty conditions. Generally speaking, every change in operating conditions and every disturbance cause pressure and flow variations or, put differently, cause the flow conditions to change with time. Flow conditions of this kind are commonly referred to as unsteady or transient. Referring specifically to pressures, they are sometimes called dynamic pressure changes

or pressure transients. The main causes of transient flow conditions are:

? Pump trip as a result of switching off the power supply or a power failure.

? Starting or stopping up one or more pumps whilst other pumps are in operation.

? Closing or opening of shut-off valves in the piping system.

? Excitation of resonant vibrations by pumps with an unstable H/Q curve.

? Variations of the inlet water level.

Fig. 2.1-b may serve as a representative example showing the pressure envelope3 with and without an air vessel following pump trip.

MKeotrteesmabove sea level

stSatetiaodny?-sretatDe rpurecskshu?rehheenaldincieurve

hNN+m

hm

Le?nnggthe

Fig. 2.1-a: Steady-state pressure head curve of a pumping system

2 Not to be confused with the term "static". 3 The term "pressure envelope" refers to the area defined by the minimum and maximum head curves along the fixed datum line resulting from all

dynamic pressures occurring within the time period under review.

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General ? The Problem of Water Hammer

2

hsteady in Fig. 2.1-b is the steadystate pressure head curve. Pressure head envelopes hminWK and hmaxWK were obtained from an installation with, hmin and hmax from an installation without air vessel. Whereas hminWK and hmaxWK are within the permissible pressure range, hmin gives evidence of vapour pressure (macrocavitation) over a pipe distance from 0 m to approximately 800 m. Almost across the entire length of the pipe, the value of hmax exceeds the maximum permissible nominal pressure of the pipe PN 16 (curve marked "PN

pipe") and is, therefore, inadmissibly high. As a rule, vapour pressure is a most undesirable phenomenon. It can have the following harmful effects:

? Dents in or buckling of thinwalled steel pipes and plastic tubes.

? Disintegration of the pipe's cement lining.

? Dirty water being drawn into drinking water pipelines through leaking connecting sockets.

We will come back to the subject of macro-cavitation, i.e. liquid column separation, in section 3.1.

Pipe length L:

2624 m

Inside diameter of pipe Di: Steady-state flow rate:

605.2 mm 500 l/s

Hpump sump: Houtlet: Air vessel inlet pipe

287.5 m 400 m

with a bypass and a non-return valve: Vair = 3.8 m3, Vwater = 6.2 m3

700 hmax

600

Metres above sea level [m]

PN Pipe

500

400 300

hmax WK hmin WK

hsteady

hmin

Elevation of pipe

200 0

500

1000

1500

Length of pipe [m]

2000

Fig. 2.1-b: Pressure head envelope of pressure transients following pump trip

2500

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Water Hammer ? Inertia

3 Water hammer

Pressure transients are also referred to as surge pressure or, if referring to water systems, water hammer. The latter term suitably reflects the harmful effects that the hammer-like blows accompanying the pressure surges can have on pipes and system components. Water hammer causes piping, valves, pipe fixtures, supports, system components, etc. to suffer the added strain of dynamic loads. The term "water hammer" is used to describe the phenomenon occurring in a closed conduit when there is either an acceleration or retardation of the flow. In contrast to a force, pressure is non-directional; i.e. it does not have a vector. Not until a hydrostatic pressure starts acting on a limiting area, is a force exerted in the direction of the area normal.

As it is not possible to altogether avoid pressure transients when operating a piping system, the art lies in keeping the pressure transients within controllable limits. What makes matters even more complex is the fact that the damage caused by impermissibly high surge pressures is not always visible. Often the consequences do not become apparent until long after the event, for example a pipe rupture, loose or disconnected flanges. The root cause of damage then tends to remain in the dark. Some representative incidents caused by water hammer are listed in the following:

Pressure rise:

? Pipe rupture

? Damaged pipe fixtures

? Damage to pumps, foundations, pipe internals and valves

Pressure fall:

? Buckling of plastic and thinwalled steel pipes

? Disintegration of the cement lining of pipes

? Dirty water or air being drawn into pipelines through flanged or socket connections, gland packing or leaks

? Water column separation followed by high increases in pressure when the separate liquid columns recombine (macro-cavitation)

3.1 Inertia

The sudden closure of a valve in a pipeline causes the mass inertia of the liquid column to exert a force on the valve's shut-off element. This causes the pressure on the upstream side of the valve to increase; on the downstream side of the valve the pressure decreases. Let us consider an example: for a DN 200 pipe, L = 900 m, v = 3 m/s, the volume of water in the pipeline is calculated by

mwater

= 0?.?2?2?4

?

900

?

1000

=

28274

kg

(1)

This is more or less the same as the weight of a truck; v = 3 m/s corresponds to 11 km/h. In other words, if the flow is suddenly stopped, our truck ? to put it in less abstract terms ? runs into a wall (closed valve) at 11 km/h (water mass inside the pipe). In terms of our pipeline, this means that the sequence of events taking place inside the pipe will result in high pressures and in high forces acting on the shut-off valve.

As a further example of inertia, Fig. 3.1-a shows a pump discharge pipe. At a very small moment of inertia of pump and motor, the failing pump comes to a sudden standstill, which has the same effect as a suddenly closing gate valve, only this time on the downstream side of the gate valve. If mass inertia causes the fluid flow on the downstream side of the pump to collapse into separate columns, a cavity containing a mixture of water vapour and air coming out of solution will be formed. As the separate liquid columns subsequently move backward and recombine with a hammerlike impact, high pressures develop. The phenomenon is referred to as liquid column separation or macro-cavitation4.

4 Macro-cavitation in pipelines is not to be confused with microscopic cavitation causing pitting corrosion on pump and turbine blades. The latter always strikes in the same place and is characterised by local high pressures of up to 1000 bar or more that develop when the microscopically small vapour bubbles collapse. With macro-cavitation, repetitive strain of this kind, or the bombarding of a sharply contoured area of the material surface, does not occur since the pressure rises are considerably lower.

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Elasticity of Fluid and Pipe Wall

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1. Steady-state condition prior to pump trip

2. Formation of a vapour pocket (cavitation cavity) following pump trip

Fig. 3.1-a: Macro-cavitation following pump trip

3. High-impact reunion of separate liquid columns accompanied by surge pressures

3.2 Elasticity of fluid and pipe wall

The attempt at visualising water hammer resulting from the inertia of a body of water made in section 3.1 is only partly correct, because no allowance was made for the elasticity of fluid and pipe wall. As long as safety belts are worn and the barrier impact speed is not too high, even a head-on collision will not put drivers in too much danger today, because the vehicle's momentum is converted to harmless deformation heat5. Contrary to the body of a car, however, water and pipe walls are elastic, even though they are so hard that this property is not noticeable in every day use.

What actually goes on inside the pipe will, therefore, be described using the following example of a heavy steel spring sliding through a pipe. This spring suffers elastic deformation when it is suddenly stopped (Fig. 3.2-a):

s1 in t1

s2 in t2

s3 in t3

Fig. 3.2-a: Sudden closure of gate valve, visualised by a heavy steel spring

The front end deformation travels in the opposite direction to the original direction of movement at the speed typical for the steel spring, i.e. wave propagation velocity a in m/s. In the compression zone, the velocity of the steel spring is v = 0 everywhere.

Following these, admittedly poor but hopefully helpful, examples chosen to illustrate the subject, we will now go back to the real situation inside the pipe,

which is shown in Fig. 3.2-b, with friction being neglected. The shut-off valve installed at the downstream end of a horizontal pipeline with a constant inside diameter, which is fed from a reservoir at constant pressure, is suddenly closed:

5 To withstand the regular pushing and shoving over rare parking spaces, cars have to be elastic. To minimise the damage of a collision at high speed, however, carmakers spend vast amounts of time and money to make their products as inelastic as possible!

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